Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page vii
... Circumference of a Circle , 116 To find the Diameter of a Circle , 116 To find the length of an Arc , Arca of a Circle , Area of a Sector , ..... Area of a Segment , .... Area of a Circular Ring ,. 117 117 118 118 119 PAGE . Area of the ...
... Circumference of a Circle , 116 To find the Diameter of a Circle , 116 To find the length of an Arc , Arca of a Circle , Area of a Sector , ..... Area of a Segment , .... Area of a Circular Ring ,. 117 117 118 118 119 PAGE . Area of the ...
Page 59
... circumference . 3. A DIAMETER is a straight line drawn through the centre and terminating in the circumference . All radii of the same circle are equal . All diameters are also equal , and each is double the radius . 4. An ARC is any ...
... circumference . 3. A DIAMETER is a straight line drawn through the centre and terminating in the circumference . All radii of the same circle are equal . All diameters are also equal , and each is double the radius . 4. An ARC is any ...
Page 60
... circumference , and whose sides are chords . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are all in the circum- ference . The sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11 ...
... circumference , and whose sides are chords . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are all in the circum- ference . The sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11 ...
Page 61
... circumference , into two equal parts . Let AEBF be a circle , and AB any diameter : then will it divide the circle and its circumference into two equal parts . A F B For , let AFB be applied to AEB , the diameter AB remaining common ; E ...
... circumference , into two equal parts . Let AEBF be a circle , and AB any diameter : then will it divide the circle and its circumference into two equal parts . A F B For , let AFB be applied to AEB , the diameter AB remaining common ; E ...
Page 62
... circumference in more than two points . Let AEBF be a circumference , and AB a straight line : then AB cannot meet the circumference in more than two points . For , suppose that they could meet in three points . We should then have ...
... circumference in more than two points . Let AEBF be a circumference , and AB a straight line : then AB cannot meet the circumference in more than two points . For , suppose that they could meet in three points . We should then have ...
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Common terms and phrases
ABē ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence